Police took the usual step of issuing the warning via Twitter, which members and supporters of the hacking groups have often used to seek publicity and communicate.

It follows the court appearance on Monday of Jake Davis, an 18-year-old from Shetland who is alleged to have been a leading member of LulzSec. He faces five related charges, including conspiracy to attack the Serious Organised Crime Agency’s website.

It also warned that targeting organisations outside Britain does not mean that hackers cannot be prosecuted under British law. Since it emerged in April, LulzSec has claimed credit for denial of service attacks on the CIA website, and network security breaches at the American broadcaster Fox and News International.

“Under UK legislation, it is an offence if a person acts from within the UK upon a computer anywhere else in the world,” the Met said.

“It is also an offence if someone anywhere else in the world to criminally affect a computer within the UK.”

The Met’s comments appear designed to caution would-be hacktivists against the idea that denial of service attacks or network security breaches are a form of legitimate civil disobedience. Anonymous in particular has styled itself as a protest movement, inviting supporters to “rise up” and warning organisations that “we the people” are “silent no more”.

Professor Peter Sommer, a cyber security expert at the London School of Economics and expert witness in computer hacking trials, said that in some ways the activities of Anonymous and LulzSec are like civil disobedience, but pointed out that real world protestors are sometimes convicted of crimes and locked up.

“A useful analogy is with Greenpeace and others who follow the line that what they do to disrupt their targets follows the Ghandi tradition of civil disobedience,” he said.

“But there is no criminal defence on that basis. They may just feel like disruption they cause is worth the sentence they get.”

“Having read many of these groups’ postings it’s clear they’re also doing it because they think it’s fun. It’s the hacker arrogance syndrome that we’ve seen many times before,” he said.

The Met’s Police Central e-Crime Unit has so far arrested three teenagers, of which two have been charged, and one bailed pending further inquiries in relation to LulzSec’s activities.

A further six people have been arrested in relation to denial of service attacks by Anonymous against corporations that withdrew services to WikiLeaks last year, including PayPal.